Remember, too, that when you add "just a bigger engine and transmission", you're not really adding just that. EVERYTHING associated with them is now bigger and heavier. That goes from the starter, alternator, usually even battery, to the motor mounts (which are probably fluid-filled in the NSX, if I were to make a guess... which I just did). Also, the bigger engine and transmission are spinning (usually) a bigger flywheel and clutch, transmitting the power through thicker (so heavier) half-shafts, spinning heavier-duty hubs, which carry bigger, heavier rotors, bigger (heavier) calipers, pads, and so on, all the way out to the 5-lug (instead of our four) wheels, which are usually 16, 17, or 18 inchers, or even more - and so, of course, heavier. And the big wheels are shod with big tires, which are - you guessed it - heavier.
And that's just the stuff on the mechanical end. Oh, figure in bigger radiators, probably a transmission oil cooler, extra plumbing for the cooling system (mid-engine, remember), and so on, and you see the weight savings really start to add up - to more weight!
I'd bet that the NSX, being a "luxury" sports car, also uses heavier glass all around, thicker carpet, and as mentioned in one of the other posts, more sound deadening materials.
When people call the NSX a lightweight sports car, they're comparing it to others within its genre; cars that typically come up in a comparison with the NSX are the Porsche 911 and Boxster, Toyota Supra, Nissan 300ZX (or 350Z now), and the Corvette. To some extent, lower-line Ferraris also get compared. Now, when thrown in with those cars (all of which, to the best of my knowledge, weigh in at 3200 lbs or more, and most tip the scales at 3500 lbs or better), the NSX *IS* a light car.
Make more sense now?
Mike